Assuming most everything else plays out as it did in OTL, then I'd put my money on either Edmund of Langley or Henry of Monmouth.
Edmund has a claim by blood proximity and he was named as heir in Richard II's OTL will. Richard also named Edmund keeper of the realm ahead of both his 1394 and 1399 OTL Irish campaigns -- this may seem like a minor point, but this position had heretofore always gone to the person highest in the succession still in England. (Even the child Thomas, future duke of Gloucester, was made keeper of the realm when Edward III and all his four older sons were out of the country.) Richard also made a show out of "adopting" Edmund's son, Edward, as his brother in the 1390s. So, clearly this was the preferred line for OTL Richard and, as the only adult line in ATL, their succession would avoid a minority. There are drawbacks here, though: 1) Edmund is elderly and in poor health, 2) Edward has no heirs, and 3) Richard has a taint of bastardy. And so, maybe Richard would look elsewhere in ATL ...
Monmouth has a claim as heir male, and Richard and Monmouth were very fond of one another in OTL. I think it's possible Richard could "adopt" Monmouth as his son -- similar to how Richard "adopted" Norwich as his brother in OTL -- in an ATL where Bolingbroke is dead so early. Richard did recognize the Lancaster as his heir in an on-again-off-again sort of way in OTL -- never fully committing because of his hatred for Bolingbroke. Here, there's nothing stopping him from going all the way. There are three major benefits for ATL Richard in doing this: 1) It settles the succession on the heir male -- a more straightforward claim than that of York's, 2) it brings the unwavering support of John of Gaunt and the vast Lancastrian network of allies to Richard's side, and 3) it threatens the lords with a minority if Richard is ever deposed for his tyranny. This seems like a very Ricardian move.
Mortimer has a claim as heir general, but is in the weakest position here, as he was in OTL. A 1390 POD means that the Mortimers are already high on Richard's enemies list and, as such, the 4th earl has likely been dispatched to Ireland in the early-1390s -- as he was in OTL -- to get him out of the way. This assignment keeps the 4th earl from building an affinity in England, and is thus much less connected than either Lancaster or York to the great families whose support is needed at this time. And, of course, the 5th earl is a child.
I’m not sure it seems he alternated between the Mortimer’s and the Yorks, the latter because he really liked Edward of Norwich
I think that the Yorks were the only part of his family to never rebel was as much a part of Richard's favor as any personal relationship between him and Edward. Bolingbroke was of course one of the junior appellants, but just as importantly, Sir Thomas Mortimer, uncle of the 4th earl of March, led a contingent of Mortimer men in Bolingbroke's army. The 4th earl of March was a child and Richard was in the process of busting up the boy's estates to parcel them out to his favorites, driving Thomas Mortimer to join the rebellion to protect his nephew's inheritance. Mortimer rather viciously slew one of Richard's favorites at the Battle of Radcot Bridge and Richard, naturally, never forgave him. The 4th earl, upon reaching his majority, protected his uncle from Richard's wrath, which put a target on his back. (Some historians speculate that Richard's 1399 Irish campaign was simply an excuse to take an army to Ireland and destroy the Mortimers -- the announcement of the campaign coming after Bolingbroke and Mowbray had been sentenced to exile, but before news of the earl's death in Ireland had reached England.)
So, with both the families of the heir general and the heir male having rebelled in the past -- where else but York could the paranoid Richard allow the crown to go? His Holland half-brothers had a
very distant claim as sons of Joan of Kent, but even they had a rocky relationship with Richard at times. (The Hollands never took up arms against him, but even they broke from him politically in the mid- to late-80s.)
